Having established the Gibbs posterior as the valid belief update for the Cut-model loss,
we now point to some other related belief updates for prequentially additive losses. These are variants of \(\eta \) -SMI, a family of belief updates introduced in [1]}.
We define three families of candidate posterior distributions interpolating between the full-Bayes posterior (REF ) and the Cut-model posterior in (REF ). The idea here, following [1]}, is to provide modulated input to the \(\varphi \)  inference from the \((\varphi ,\theta ,Y)\) -module. In the next section we motivate this step in a bit more detail.
